This is a question about terminology related to orbit stability.

I had wanted to ask about stability of orbits described in the paper Three Classes of Newtonian Three-Body Planar Periodic Orbits Milovan Šuvakov and V. Dmitrašinović Phys. Rev. Lett. 110, 114301



until I realized I am not even sure what could be meant by "stable". In the circular restricted three-body problem, there are periodic orbits around libration points that are said to be exponential unstable. In that context, I believe it means that without perturbation the orbits would continue in perpetuity, but any small perturbation would cause the orbit to deviate exponentially with time. For example a Halo orbit around Sun-Earth L1 may have a period of six months, but the doubling time of any deviation may only be two weeks.

I have looked at On the stability of the three classes of Newtonian three-body planar periodic orbits Li, X. & Liao, S. Sci. China Phys. Mech. Astron. (2014) 57: 2121. doi:10.1007/s11433-014-5563-5


which seems to suggest that many of the orbits described by Šuvakov and Dmitrašinović will eventually diverge if careful numerical integration is applied.

It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time, and are thus most possibly unstable at least.

If that is true, does that mean those orbits are said to be periodic but unstable, or only approximately periodic?

Then I read the following sentence in the abstract of Marija R. Janković and V. Dmitrašinović, Phys. Rev. Lett. 116, 064301 (2016)


This regularity supports Hénon’s 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol’mogorov-Arnol’d-Moser, stable.

The page Asymptotic Stability also mentions Lyapunov stability.

Question: I would like to know: what are the different terms related to "stability" that can apply to planar periodic orbits, and what do they mean?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.